Question

which angles are supplementary to \\( \angle 4 \\)? select all that apply.

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Identify adjacent angles forming a linear pair with \(\angle4\)

\(\angle2\) and \(\angle4\) form a linear pair (sum \(180^{\circ}\)). Also, \(\angle4+\angle5+\angle6 = 180^{\circ}\) (straight - line angle). But if we consider the straight - line formed by the intersection of lines, \(\angle3\) and \(\angle4\) are not adjacent. Wait, no. Wait, in a general intersection of lines, \(\angle2\) and \(\angle4\) are adjacent and form a linear pair (\(\angle2+\angle4 = 180^{\circ}\)). Also, \(\angle3\) and \(\angle4\) are not adjacent. Wait, no, actually, if we consider the full - circle around the point of intersection (sum \(360^{\circ}\)), but for supplementary angles (sum \(180^{\circ}\)). Another way: \(\angle4\) and \(\angle2\) are adjacent supplementary (linear pair). Also, \(\angle4\) and \(\angle6\) (because \(\angle2=\angle6\) (vertical angles), and \(\angle2+\angle4 = 180^{\circ}\), so \(\angle6+\angle4=180^{\circ}\))

Answer:

\(\angle2\) and \(\angle6\)